The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual

Abstract

In this paper we prove that the Dunkl intertwining operator Vk defined only on the space of polynomials on can also be extended to an operator on spaces of functions and distributions. We study also its dual tVk and we prove that for each there exists a positive measure vy on the Borel ω-algebra of with support in such that for all function f continuous on and with compact support, we have